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Sequence

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February 21, 2016
SequencePerfect SquaresIntegersnumber theory with sequences

Problem Statement

The sequence xnx_{n} is de fined by: x0=1,x1=0,x2=1,x3=1,xn+3=(n2+n+1)(n+1)nxn+2+(n2+n+1)xn+1−n+1nxn(n=1,2,3..)x_{0}=1, x_{1}=0, x_{2}=1,x_{3}=1, x_{n+3}=\frac{(n^2+n+1)(n+1)}{n}x_{n+2}+(n^2+n+1)x_{n+1}-\frac{n+1}{n}x_{n} (n=1,2,3..)
Prove that all members of the sequence are perfect squares.
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